# Homework Help: Proving that this set is a Dedekind cut.

1. Apr 17, 2012

### jdinatale

1. The problem statement, all variables and given/known data

2. Relevant equations

In the above proplem, A is a dedekind cut.

To be a cut:
1. $A \not= \mathbf{Q}$ and $A \not = \emptyset$
2. If $r \in A$, then all $s \in A$ for all $s \in \mathbf{Q}$ such that $s < r$
3. A has no maximum

I know the 3 properties by heart, but the set -A is so unwieldy, that I'm having difficulty proving each of these properties.

2. Apr 17, 2012

### Hurkyl

Staff Emeritus
Then try things step-by-step. First, carefully write out what it is to be proven, incorporating the definition of -A....